Problem: Which of the following ordered pairs represents a solution to the equation below? $(-2, -3) (-1, -2) (0, 2) (1, 3) (2, 5)$ $y = 3x+1$
Answer: We can try plugging in the x-value of each ordered pair into the equation. If we evaluate and get the y-value of the ordered pair, then that ordered pair is a solution! Let's consider $(-2, -3)$ If we plug in $-2$ for $x$ and evaluate, do we get $-3$ $y = (3)(-2) + 1 = -6 + 1 = -5$ Let's consider $(-1, -2)$ If we plug in $-1$ for $x$ and evaluate, do we get $-2$ $y = (3)(-1) + 1 = -3 + 1 = -2$ Let's consider $(0, 2)$ If we plug in $0$ for $x$ and evaluate, do we get $2$ $y = (3)(0) + 1 = 0 + 1 = 1$ Let's consider $(1, 3)$ If we plug in $1$ for $x$ and evaluate, do we get $3$ $y = (3)(1) + 1 = 3 + 1 = 4$ Let's consider $(2, 5)$ If we plug in $2$ for $x$ and evaluate, do we get $5$ $y = (3)(2) + 1 = 6 + 1 = 7$ Thus the only ordered pair that is a solution to the equation is $(-1, -2)$ We come to the same answer by plotting the points and the equation. $2$ $4$ $6$ $8$ $\llap{-}4$ $\llap{-}6$ $\llap{-}8$ $2$ $4$ $6$ $8$ $\llap{-}4$ $\llap{-}6$ $\llap{-}8$